The invention relates to cervical intervertebral prostheses which have a predefined center of the hinge movement. In a first known type of such prostheses, the center of the hinge movement is located inside the prosthesis (U.S. Pat. No. 5,425,773; EP-A-1166725). This does not correspond to the natural conditions which the prosthesis is intended to simulate. In another type of intervertebral prosthesis (FR-A-2718635), the hinge is formed by a pair of slide surfaces, the common center of curvature of which lies outside the prosthesis, specifically under it. This approximates to the natural conditions but is still too far remote from them.